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We present a methodology to analyse and interpret a set of telescopic observations of the mutual orbital phenomena between Jupiter’s Galilean satellites (occultation and eclipses) as a practical teaching tool for photometry and astrodynamic studies in astronomy courses. The mutual phenomena we describe took place in 2014 and 2015 and the observations were obtained using a 28 cm aperture telescope and a video camera. We introduce simple models to explain occultation and eclipses of the events, and offer the data and the software for their analysis. [ABSTRACT FROM AUTHOR]